Question

4.2 theoretical probability. calculating theoretical probabilities (other). in the game of roulette, there is a wheel with spaces marked 0 through 36 and a space marked 00. a) find the probability of winning if you pick the number 27 and it comes up on the wheel. leave your answer as a fraction. b) find the probability of an odd number coming up on the wheel. leave your answer as a fraction. question help: video 1 video 2 message instructor submit question

Explanation:

Step1: Calculate total number of outcomes

The wheel has spaces marked 0 - 36 and 00, so there are $36 + 1+1=38$ total outcomes.

Step2: Calculate probability for part a

There is only 1 favorable outcome (the number 27). The probability formula is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So for picking 27, $P=\frac{1}{38}$.

Step3: Calculate number of odd - numbered outcomes for part b

The odd numbers from 0 to 36 are 1, 3, 5, …, 35. The formula for the number of terms in an arithmetic sequence $a_n=a_1+(n - 1)d$ where $a_1 = 1$, $d = 2$, $a_n=35$. Solving $35=1+(n - 1)\times2$ gives $n = 18$. So there are 18 odd - numbered outcomes.

Step4: Calculate probability for part b

Using the probability formula $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$, the probability of getting an odd number is $P=\frac{18}{38}=\frac{9}{19}$.

Answer:

a) $\frac{1}{38}$
b) $\frac{9}{19}$